Problem: $\dfrac{9}{4} \div \dfrac{7}{4} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{7}{4}$ is $\dfrac{4}{7}$ Therefore: $ \dfrac{9}{4} \div \dfrac{7}{4} = \dfrac{9}{4} \times \dfrac{4}{7} $ $ \phantom{\dfrac{9}{4} \times \dfrac{4}{7}} = \dfrac{9 \times 4}{4 \times 7} $ $ \phantom{\dfrac{9}{4} \times \dfrac{4}{7}} = \dfrac{36}{28} $